الفهرس 
Some perturbation techniquesOnly 14 pages are availabe for public view
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Abstract
The study and utilization of pendulum motion attracts the attention of many researchers due to its numerous applications in various fields, because of its significance in a wide range of industrial applications, including data gathering, and building. To investigate the motion, some important perturbation methods must be explained.
In this thesis, two different significant models are examined. The first one investigates the planar motion of a dynamical system of 3DOF triple pendulum, consisting of two rigid pendulums attached to a single un-stretched pendulum in which its suspension point is considered to be fixed. Using Lagrange’s equations, the EOM of the controlling system are derived. The MST is applied to achieve the analytic solutions of these equations up to higher order of approximation as novel approximate solutions. The accuracy of these solutions is proven by comparing them with the numerical results of the EOM. The system’s resonance cases are characterized, and its modulation equations are confirmed. In light of solvability conditions, the steady-state solutions are examined. A graphic depiction of the dynamical behavior regarding the motion time histories and resonance curves is illustrated. The stability zones are described and explained by analyzing their graphs to evaluate the positive effect of different parameters on the dynamical behavior.
The second model studies the planar motion of a dynamical model with 2DOF consisting of a connected tuned absorber with a simple pendulum. It is taken into account that the pendulum’s pivot moves in a Lissajous trajectory with stationary angular velocity in the presence of a harmonic excitation moment. Equations of Lagrange are used to derive the motion controlling system. The approximate solutions of these system up to third order of approximation are achieved utilizing the MST. All cases of resonance are categorized; in which two of them are examined simultaneously to gain the corresponding equations of modulation. The solutions at the steady-state solutions are studied in terms of solvability conditions. According to RHC, all potential fixed points at steady and unsteady states are determined and graphed. The dynamical behavior of time histories of the motion and the curves of resonance are drawn. Regions of stability are examined by inspecting their graphs in order to assess the favorable impact of various parameters on the motion.